The (weak) Nullstellansatz: If $A$ is a finitely generated $\mathbb{C}$-algebra, then $A$ is the zero ring if and only if $\mathrm{Hom}(A, \mathbb{C})$ is empty.
More generally, if $A$ and $B$ are finitely generated $\mathbb{C}$-algebras without nilpotents, then a map $A \to B$ is determined by the map $\mathrm{Hom}(B, \mathbb{C}) \to \mathrm{Hom}(A, \mathbb{C})$ that it induces.
